Other mistake: In the scene where Bateman is about to murder Paul Allen, he turns on the CD player and walks towards the axe meaning to say "...song's so catchy;" but if you watch his mouth, you can see that in place of the word "catchy" there is a blatant voiceover. Who knows what he said in the original shooting. (00:28:25)
Other mistake: Several close-ups of the business cards of Patrick Bateman and his associates reveal a misspelling of the word "Acquisitions" (the "c" is missing - not a small error, given that this is the name of their department).
Answer: The situation is intentionally left vague. The homeless man being murdered wouldn't necessarily make the news in the time (there were over 4000 murders in 1989-90 when the book and movie are set). He and his friends are so alike that they continually mistake each other for others. The prostitutes would likely be loathe to call the police because they might be arrested themselves and he would likely get off with a much better lawyer.
Greg Dwyer